integral of ln(x)ln(x)

Lösung

\int ln (x) ln (x) d x

x ln^{2} (x) - 2 x ln (x) + 2 x + C

Schritte zur Lösung

\int ln (x) ln (x) d x

Wende die partielle Integration an

= ln (x) (x ln (x) - x) - \int ln (x) - 1 d x

\int ln (x) - 1 d x = x ln (x) - 2 x

= ln (x) (x ln (x) - x) - (x ln (x) - 2 x)

Vereinfache

ln (x) (x ln (x) - x) - (x ln (x) - 2 x) : x ln^{2} (x) - 2 x ln (x) + 2 x

= x ln^{2} (x) - 2 x ln (x) + 2 x

Füge eine Konstante zur Lösung hinzu

= x ln^{2} (x) - 2 x ln (x) + 2 x + C

\int 1 + x^{4} d x

\frac{\partial}{\partial x} (3 x e^{4 x y})

\int \frac{11 x}{x ^{2} + 1} d x

w \to 0 lim (\frac{e ^{2 w} - ( 1 + w )}{w ^{2}})

\int \frac{1}{- x} d x